Question

1. select the velocity vs time graph that best matches the position versus time graph shown below.
2. suppose you are given a position versus time graph. what is the slope of the graph? a. displacement b. velocity c. acceleration d. time

Explanation:

Step1: Recall the relationship between position - time and velocity - time graphs

The slope of a position - time graph gives velocity. If the position - time graph is a straight line with a constant positive slope, it means the object is moving with a constant positive velocity.

Step2: Analyze the given position - time graph

The given position - time graph is a straight line with a non - zero constant slope. This implies a constant non - zero velocity.

Step3: Match with velocity - time graphs

Among the options, a constant non - zero velocity is represented by a horizontal line on a velocity - time graph. Option c shows a horizontal line above the time - axis, which represents a constant positive velocity.

For question 12:
The slope of a position versus time graph is defined as $\text{slope}=\frac{\Delta x}{\Delta t}$, where $\Delta x$ is the change in position (displacement) and $\Delta t$ is the change in time. By the definition of velocity $v = \frac{\Delta x}{\Delta t}$, the slope of a position - time graph is velocity.

Answer:

1. c.
2. b. Velocity